Two sections (2) which are to be glued together are laid next to each other transversely on a machine. The chassis (21) of the machine (20) carries means of supporting the band; means of pressing against the side of the band that is not glued to apply it to a surface between the means of support and a heater (30) to activate the glue. A continuous process of sticking together a band to form a watertight and insulating wall, using rectangular panels containing layers of impermeable material. Two adjacent panels are stuck together using a flexible band containing at least one fine metallic layer by continuous application of polymerizable or thermofusible glue to the band or the panels; continuous pressing of the band against the adjacent edges and continuous heating of the band in contact to activate the glue, before or after the pressing action. In addition a final cooling stage solidifies the glue. The glue can be applied to the band as it is stuck to the panels, or if thermofusible glue is used, it can be applied at a temperature at which it is fluid, before the band is cooled and wound onto a bobbin. The band can then be unrolled, heated to a second temperature less than or equal to the first to reactivate the glue as it is pressed continuously onto the panel edges. Independent claims are included for; (1) The machine (20) has a tubular chassis (21) with at least two longitudinal elements (22) connected to each other by at least one transverse element (23, 24). Rollers (26) are connected to the chassis along its longitudinal axis (L) so they roll against the surface (14) of two sections (2) which are to be glued together. The band is held by at least two longitudinal retaining pieces parallel to the axis of rotation of the rollers, with the active parts of the retaining pieces extending transversely outside the machine. The machine is automobile, with the chassis including a drive motor (84). The drive mechanism includes rollers (85) placed along the longitudinal axis near the means holding the band, with the rollers driven in rotation by the drive motor about an axis of rotation perpendicular to that of the rollers (26). The drive rollers can be moved between an active position against the walls (10) and a retracted position away from the walls. This movement is controlled by engaging and disengaging with longitudinal grooves (13). The heater is placed between the longitudinal elements, where the band is received, so it can heat the band using at least one resistance (32) and a ventilation system (33) which blows air across the resistance to form a flow of hot air towards the band. The heater can be placed upstream of the glue applicator (68) to speed the polymerisation of the glue. In this case, the heater is a temperature-controlled hot iron. Glue is applied to one side of the band (8) between the longitudinal elements. The band is held by a pressing roller whose distance in plan from the chassis is variable and which is designed to press the band against the glued surface. Coolers are mounted on the chassis between the longitudinal elements downstream of the heaters and glue application to accelerate the curing process; and (2) Insulating and watertight wall made using this process and / or machine.